What convex geometries tell about shattering-extremal systems

DOI10.37236/10750zbMath1496.05181OpenAlexW4293062877WikidataQ114023886 ScholiaQ114023886MaRDI QIDQ2170793

Bogdan Chornomaz

Publication date: 6 September 2022

Published in: The Electronic Journal of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.37236/10750

zbMATH Keywords

Hamming distanceforbidden projectionsshattering-extremal closure system

Mathematics Subject Classification ID

Axiomatic and generalized convexity (52A01) Extremal set theory (05D05) Combinatorial aspects of matroids and geometric lattices (05B35)

Cites Work

• Shattering-extremal set systems of VC dimension at most 2
• A new look at the Jordan-Hölder theorem for semimodular lattices
• The theory of convex geometries
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• Meet-distributive lattices and the anti-exchange closure
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• On the trace of finite sets
• Join-semidistributive lattices and convex geometries.
• Defect Sauer results
• Unlabeled sample compression schemes and corner peelings for ample and maximum classes
• Shattering-extremal set systems from Sperner families
• Unlabeled compression schemes exceeding the VC-dimension
• Optimum basis of finite convex geometry
• A combinatorial problem; stability and order for models and theories in infinitary languages
• On the density of families of sets
• Some Combinatorial Applications of Gröbner Bases
• A Geometric Approach to Sample Compression
• A Computing Procedure for Quantification Theory
• A machine program for theorem-proving
• On the Uniform Convergence of Relative Frequencies of Events to Their Probabilities

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